Descriptive statistics, such as median and outliers, need to be determined before the functional data can be displayed for exploratory data analysis. Ordering the samples of curves and images directly is difficult. Therefore, many functional depths have been proposed that establish the center of the functional data sample and then order them from the center outwards. Available functional depths in a marginal perspective are the integrated depth ([1]} [1]}), random projection depth ([3]} [3]}), random Tukey depth ([5]} [5]}), band and modified band depth ([7]} [7]}), half-region depth and modified half-region depth ([9]} [9]}), functional spatial depth ([11]} [11]}), and extremal depth ([13]} [13]}). Moreover, multivariate functional depths have been proposed based on two generalizations: from functional to multivariate functional scenarios and from multivariate to multivariate functional scenarios. Examples of the first idea include the weighted average of the marginal functional depths ([15]} [15]}) and the simplicial and modified simplicial band depths ([17]} [17]}). An example of the second idea is the multivariate functional halfspace depth ([19]} [19]}). With the intensive development of different data depth notions, various tools have been developed for visualizing functional data and detecting outliers.
